Probability that you purchase x boxes that do not have the desired prize is [tex](0.9)^{x}[/tex]
Probability:
Probability is a measure of the likelihood of an event to occur.
For the given question,
Let us assume,
[tex]P_{1}[/tex] = Probability that a randomly selected box of a certain type of cereal has a particular prize is .1
[tex]P_{2}[/tex] = Probability that you purchase x boxes that do not have the desired prize
= 1 - [tex]P_{1}[/tex]
= 1 - 0.1
= 0.9
(a). We have to find probability that you purchase x boxes that do not have the desired prize
= Probability of not getting prize x times
= 0.9 * 0.9 * 0.9 * 0.9 ........... x times
= [tex](0.9)^{x}[/tex]
Thus,
Probability that you purchase x boxes that do not have the desired prize is [tex](0.9)^{x}[/tex]
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